\section{Insurer Operating Results By Population Loss Ratio Estimate}
\label{sec:InsurerOperatingResultsByPopulationLossRatioEstimate}

Insurers' variable claims costs determine whether they succeed or fail: Are they profitable? Are they incurring operating losses? Are they solvent? What level of benefits can they provide? What are the highest level of claims costs they can pay and survive? Insurers earn profits, or at least avoid losses, if the sum of their Population Loss Ratio Estimates and their operating expense ratios are less than, or equal to, 100\% (i.e. Claims Costs + Operating Expenses $\leq$ Earned Premiums). If their Population Loss Ratio Estimates and operating expense ratios exceed their premium revenues, insurers incur Operating Losses. If an insurer's claims costs and operating expenses greatly exceed their premium revenues insurers, they may become insolvent, unable to pay their obligations, and should cease their insurance operations. 

\subsection{Insurer Operating Results By Portfolio Size - Profits}
\label{sec:InsurerOperatingResultsByPortfolioSize-Profits}

All insurers earn profits according to these relationships:
\begin{center}
\noindent Profit $\geq$ (Profit Margin + Risk Premium) IF Claims Costs $\leq$ Expected Claims Costs \newline

\noindent Profit $\geq$ Profit Margin IF Claims Costs $\leq$ (Expected Claims Costs + Risk Premium) \newline

\noindent Profit $\geq$ 0 IF Claims Costs $\leq$ (Expected Claims Costs + Profit Margin + Risk Premium) 
\end{center}

\subsection{Insurer Operating Results By Population Loss Ratio Estimate - Losses}
\label{sec:InsurerOperatingResultsByPopulationLossRatioEstimate-Losses}

Insurers incur operating losses (Claims Costs $>$ Expected Claims Costs + Profit Margins + Risk Premiums). Insurers become insolvent when their claims costs are so high that they have insufficient resources to pay all their obligations. Insolvent insurers should close their doors, but may continue their under-capitalized operations for many years, as may insolvent health care providers. Insolvent insurers (health care providers) put policyholders (patients) at risk for denied or delayed care due to insurer (provider) malfeasance or negligence.

Insurers can prevent insolvency by maintaining highly liquid assets called ``Surplus,'' so they can cover higher than expected claims costs. Insurers cannot prevent all their risk of insolvency because the more surplus they maintain the less efficient they become as continuing enterprises. The highly liquid assets devoted to surplus are not available to produce the usual goods or services an enterprise furnishes, so allocating resources to surplus removes them from more productive operations. In effect, the greater the value of resources devoted to surplus the lower the solvency risk and the lower the profits of the insurer. 

Most States have minimal statutory surplus requirements, but these minimum requirements, usually specific dollar values of assets, do not offer equivalent levels of insolvency risk protection for all insurers. Large insurers tend to require lower amounts of surplus funds while small insurers may require far higher than statutory surplus. To compare insurers on a level playing field I will require all insurers to protect themselves from insolvency with the same probability, 0.9987, by maintaining surplus assets sufficient to cover all claims cost from Population Loss Ratio Estimates at, or below three standard errors above the Population Loss Ratio. 

